Recent multi-wavelength observations indicate that some starburst galaxies show a dominant nonthermal contribution from its central region. These active galactic nuclei (AGN)-starburst composites are of special interest, as both phenomena on their own are potential sources of the high-energetic cosmic rays and their accompanied gamma-ray and neutrino emission. Here, we will focus on NGC 1068, which is known since several years from its atypical radio-gamma-ray correlation. Recently this source has also shown strong indications of high energy neutrino emission. A first semi-analytical, two-component multi-messenger model is presented that already gives some constraints on the AGN-starburst composite characteristics of NGC 1068 and exposes the need to include both starburst and AGN corona to describe the multi-messenger data.